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<p>In this paper, we shall prove that on a non-flat Riemannian vector bundle over a compact Riemannian manifold, the smooth solution of the Yang–Mills flow will blow up in finite time if the energy of the initial connection is small enough. We also consider the finite-time blow-up for the Yang–Mills flow with the initial curvature near the harmonic form. Furthermore, when <i>E</i> is a holomorphic vector bundle over a compact Kähler manifold, <i>E</i> will admit a projectively flat structure if the trace-free part of Chern curvature is small enough.</p>

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The Finite Time Blow-up of the Yang-Mills Flow

  • 期刊论文

  • 发表日期：

    2025年1月15日

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  • Guanxiang Wang,
  • Chuanjing Zhang

摘要

In this paper, we shall prove that on a non-flat Riemannian vector bundle over a compact Riemannian manifold, the smooth solution of the Yang–Mills flow will blow up in finite time if the energy of the initial connection is small enough. We also consider the finite-time blow-up for the Yang–Mills flow with the initial curvature near the harmonic form. Furthermore, when E is a holomorphic vector bundle over a compact Kähler manifold, E will admit a projectively flat structure if the trace-free part of Chern curvature is small enough.